SOLUTION: Hello math tutor. i need help on graphing this. i need to Graph the function: the axis of symmetry, the vertex, and the x-intercepts. Problem:{{{ y=-2x^2+x-4 }}} Thank You!

Algebra ->  Test -> SOLUTION: Hello math tutor. i need help on graphing this. i need to Graph the function: the axis of symmetry, the vertex, and the x-intercepts. Problem:{{{ y=-2x^2+x-4 }}} Thank You!      Log On


   

Question 596480: Hello math tutor. i need help on graphing this. i need to Graph the function: the axis of symmetry, the vertex, and the x-intercepts.
Problem:+y=-2x%5E2%2Bx-4+
Thank You!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The axis of symmetry is a vertical line through
the x-coordinate of the vertex
The vertex is at +-b%2F%282a%29+ when the equation
is in the form +ax%5E2+%2B+b%2Ax+%2B+c+
+-b%2F%282a%29+=+-1%2F%282%2A%28-2%29%29+
+-b%2F%282a%29+=+1%2F4+
Now find +y%28+1%2F4+%29+
+y%281%2F4%29+=+-2%2A%281%2F4%29%5E2+%2B+1%2F4+-+4+
+y%281%2F4%29+=+-1%2F8+%2B+2%2F8+-+32%2F8+
+y%281%2F4%29+=+-31%2F8+
The vertex is at ( 1/4, -31/8 )
The axis of symmetry is +x+=+1%2F4+
-------------------------------
Find the x-intercepts by setting +y+=+0+
:+y+=+-2x%5E2+%2B+x+-+4+
:+-2x%5E2+%2B+x+-+4+=+0+
Use the quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+-2+
+b+=+1+
+c+=+-4+
+x+=+%28-1+%2B-+sqrt%28+1%5E2+-+4%2A%28-2%29%2A%28-4%29+%29%29+%2F+%282%2A%28-2%29%29+
+x+=+%28-1+%2B-+sqrt%28+1+-+32+%29%29+%2F+%28-4%29+
+x+=+%281+%2B+sqrt%28+31+%29+%2Ai%29+%2F+4+
and
+x+=+%281+-+sqrt%28+31+%29+%2Ai%29+%2F+4+
The roots are imaginary, so there are no x-intercepts
here's a plot:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-10%2C+2%2C+-2x%5E2+%2B+x+-+4+%29+